(again as Michelson did)
for two different observers,
which would imply that
both observers agree in their
time measurements.

These ideas were contradicted by
Michelson's EXPERIMENTS,
which were so ingeniously devised
and so precisely performed.

And so Einstein said that
instead of starting with such ideas,
and basing our reasoning on them,
let us rather
START WITH THE EXPERIMENTAL DATA,
and see to what relationships
they will lead us,
relationships between
the length and time measurements
of different observers.
Now what experimental data
must we take into account here?
They are:
FACT (1)
It is impossible
to measure the "ether wind,"
or, in other words,
it is impossible to detect our motion
relative to the ether.
This was clearly shown by the
Michelson-Morley experiment,
as well as by all other experiments
devised to
measure this motion (see Ch. I.).
Indeed, this is hte great
"conspiracy"
that started all the trouble,
or, as Einstein prefers to see it,
and most reasonably so,
THIS IS A FACT.
FACT (2)
The velocity of light is the same
no matter whether the source of light
is moving or stationary.
Let us examine this statement
more fully,
to see exactly what it means.

To do this,
it is necessary to remind the reader
of a few well-known facts:
Imagine that we have two trains,
one with a gun on the front end,
the other with a source of sound
on the front end,
say, a whistle.
Suppose that the velocity, u,
of a bullet shot from the gun,
happens to be the same as
the velocity of the sound.
Now suppose that both trains
are moving with the same velocity, v,
in the same direction.
The question is:
How does the velocity of a bullet
(fired from the MOVING train)
relatively to the ground,
compare with
the velocity of the sound
that came from the whistle
on the other MOVING train,
realtive to the medium, the air,
in which it is traveling?
Are they the same?

No!

The velocity of the bullet,
RELATIVELY TO THE GROUND,
is v + u,
since the bullet is now propelled forward
not only with its own velocity, u,
given to it by the force of the gun,
but, in addition,
has an inertial velocity, v,
which it has acquired from
the motion of the train
and which is shared by
all objects on the train.

But in the case of the sound wave
(which is a series of pulsations,
alternate condensations and rarefactions of the air
in rapid succession),
the first condensation formed
in the neighborhood of the whistle,
travels out with velocity u
relatively to the medium,
regardless as to whether
the train is moving or not.
So that this condensation
has only its own velocity
and does NOT have the inertial velocity
due to the motion of the train,
the velocity of the sound
depending only upon the medium
(that is, whether it is air or water, etc.,
and whether it is hot or cold, etc.),
but not upon the motion of the source
from which the sound started.

The following diagram
shows the relative positions
after one second,
in both cases:

Thus, in Case II.,
the bullet has moved
u + v feet in one second
from the starting point,
whereas the sound has moved only u feet
from the starting point,
in that one second.
Thus we see that
the velocity of sound is u feet per second
relatively to the starting point,
whether the source remains stationary
as in Case I.,
or follows the sound, as in Case II.

Expressing it algebraically,
x = ut
applies equally well for sound
in both Case I. and Case II.,
x being the distance
FROM THE STARTING POINT.
Indeed, this fact is true of ALL WAVE MOTION,
and one would therefore expect
that it would apply also to LIGHT.
As a matter of FACT,
it DOES,
and that is what is meant by
FACT (2) above.

Now, as a result of this,
it appears,
by referring again to the diagram above,
that
relatively to the MOVING train (Case II.)
we should then have,
for sound
x' = (u - v)t
x' being the distance
from T' to the point where
the sound has arrived after time t.
From which, by measuring x', u, and t,
we could then calculate v,
the velocity of the train.
And, similarly, for light
using the moving earth
instead of the moving train,
we should then have,
as a consequence of FACT (2) above,
x' = (c - v)t
where c is the velocity of light
(relatively to a stationary observer
out in space)
and v is the velocity of the earth
relatively to this stationary observer --
and hence
the ABSOLUTE velocity of the earth.

Thus we should be able
to determine v.
But this contradicts FACT (1),
according to which
it is IMPOSSIBLE to determine v.

Thus it APPEARS that
FACT (2) requires
the velocity of light
RELATIVELY TO THE MOVING EARTH
to be c - v (see diagram above),
whereas FACT (1) requires it to be c.
And so the two facts
contradict each other!
Or, stating it another way:

If, in one second,
the earth moves from E to E'
while a ray of light,
goes from the earth to L,
then
FACT (1) requires that
E'L be equal to c (= 186,000 miles)
while FACT (2) requires that
EL be equal to c!

Now it is needless to say that
FACTS CAN NOT CONTRADICT
EACH OTHER!

Let us therefore see how,
in the light of the discussion in Ch. III.
FACTS (1) and (2) can be shown to be
NOT contradictory.